A Data-Driven Block Thresholding Approach To Wavelet Estimation
The Annals of Statistics 36, to appear, (2008).
A Data-Driven Block Thresholding Approach To Wavelet Estimation
The Annals of Statistics 36, to appear, (2008).
- Abstract: A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by minimizing Stein's unbiased risk estimate. The estimator is sharp adaptive over a class of Besov bodies and achieves simultaneously within a small constant factor of the minimax risk over a wide collection of Besov Bodies including both the dense and sparse cases. The procedure is easy to implement. Numerical results show that it has superior finite sample performance in comparison to the other leading wavelet thresholding estimators.
- Paper: pdf file. (A longer version with detailed proofs is here.)
- Other related papers:
Cai, T. (1999).
Adaptive wavelet estimation: a block thresholding and oracle inequality approach.
The Annals of Statistics 27, 898-924.Cai, T. & Silverman, B.W. (2001).
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Sankhya 63, 127-148.Cai, T. (2002).
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Statistica Sinica 12, 1241-1273.Cai, T. & Low, M. (2005).
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